Exam 7: Potential Energy and Energy Conservation

When a particle is a distance r from the origin,its potential energy function is given by the equation ,where k is a constant and (a)What are the SI units of k? (b)Find a mathematical expression in terms of x,y,and z for the y component of the force on the particle. (c)If U = 3.00 J when the particle is 2.00 m from the origin,find the numerical value of the y component of the force on this particle when it is at the point (-1.00 m,2.00 m,3.00 m).

A 2.0 g bead slides along a frictionless wire,as shown in the figure.At point A,the bead is moving to the right but with negligible speed. (a)What is the potential energy of the bead at point A? (b)What is the kinetic energy of the bead at point B? (c)What is the speed of the bead at point B? (d)What is the speed of the bead at point C?

A particle experiences a force given by .Find the potential field U(x)the particle is in.(Assume that the zero of potential energy is located at x = 0.)

In the figure,a 4.0-kg ball is on the end of a 1.6-m rope that is fixed at 0.The ball is held at point A,with the rope horizontal,and is given an initial downward velocity.The ball moves through three quarters of a circle with no friction and arrives at B,with the rope barely under tension.The initial velocity of the ball,at point A,is closest to

Block 1 and block 2 have the same mass,m,and are released from the top of two inclined planes of the same height making 30° and 60° angles with the horizontal direction,respectively.If the coefficient of friction is the same in both cases,which of the blocks is going faster when it reaches the bottom of its respective incline?

In the figure,a very small toy race car of mass m is released from rest on the loop-the-loop track.If it is released at a height 2R above the floor,how high is it above the floor when it leaves the track,neglecting friction?

A tennis ball bounces on the floor three times.If each time it loses 22.0% of its energy due to heating,how high does it rise after the third bounce,provided we released it from the floor?

A potential energy function is given by U(x)= ( 3.00 N/m)x - ( 1.00 N/m³)x³.At what position or positions is the force equal to zero?

A box of mass m is pressed against (but is not attached to)an ideal spring of force constant k and negligible mass,compressing the spring a distance x.After it is released,the box slides up a frictionless incline as shown in the figure and eventually stops.If we repeat this experiment but instead compress the spring a distance of 2x

A box of mass m is pressed against (but is not attached to)an ideal spring of force constant k and negligible mass,compressing the spring a distance x.After it is released,the box slides up a frictionless incline as shown in the figure and eventually stops.If we repeat this experiment with a box of mass 2m

Is it possible for a system to have negative potential energy?

A 5.00-kg object moves clockwise around a 50.0 cm radius circular path.At one location,the speed of the object is 4.00 m/s.When the object next returns to this same location,the speed is 3.00 m/s. (a)How much work was done by nonconservative (dissipative)forces as the object moved once around the circle? (b)If the magnitude of the above nonconservative (dissipative)forces acting on the object is constant,what is the value of this magnitude?

A 1.86-kg block is held in place against the spring by a 81-N horizontal external force (see the figure).The external force is removed,and the block is projected with a velocity upon separation from the spring.The block descends a ramp and has a velocity at the bottom.The track is frictionless between points A and B.The block enters a rough section at B,extending to E.The coefficient of kinetic friction over this section is 0.28.The velocity of the block is v₃ = 1.4 m/s at C.The block moves on to D,where it stops.The height h of the ramp is closest to

An athlete stretches a spring an extra 40.0 cm beyond its initial length.How much energy has he transferred to the spring,if the spring constant is 52.9 N/cm?

A small hockey puck slides without friction over the icy hill shown in the figure and lands 6.20 m from the foot of the cliff with no air resistance.What was its speed v₀ at the bottom of the hill?